Perform the indicated operations and simplify the result so there are no quotients.
-$$\frac { ( \sin \theta + \cos \theta ) ^ { 2 } } { 1 + 2 \sin \theta \cos \theta }$$
A) 1
B) $- \sec ^ { 2 } \theta$
C) $1 - \sin \theta$
D) 0

Question

Quizplus · Accepted Answer

Expanding the numerator gives $\sin^2\theta + 2\sin\theta\cos\theta + \cos^2\theta$. The denominator is $1 + 2\sin\theta\cos\theta$. Since $\sin^2\theta + \cos^2\theta = 1$, the expression simplifies to $\frac{1 + 2\sin\theta\cos\theta}{1 + 2\sin\theta\cos\theta} = 1$.

Perform the Indicated Operations and Simplify the Result So There (sin⁡θ+cos⁡θ)21+2sin⁡θcos⁡θ\frac { ( \sin \theta + \cos \theta ) ^ { 2 } } { 1 + 2 \sin \theta \cos \theta }1+2sinθcosθ(sinθ+cosθ)2​

Perform the Indicated Operations and Simplify the Result So There $\frac { ( \sin \theta + \cos \theta ) ^ { 2 } } { 1 + 2 \sin \theta \cos \theta }$